Key Takeaways
- L_crit = R×(1−D) / (2×f)
- L > L_crit → CCM; L < L_crit → DCM
- Light load requires larger inductance to maintain CCM
Lesson 4
Critical Inductance: The CCM/DCM Boundary
Critical inductance L_crit is the value where inductor current minimum just touches zero. L > L_crit means CCM, L < L_crit means DCM.
The CCM condition is inductor current minimum > 0. Minimum = average current − ΔI/2 = VOUT/R − (VIN−VOUT)×D/(2×f×L). Setting minimum = 0 and solving for L gives the critical inductance.
Simplifying: L_crit = R×(1−D) / (2×f). Note it depends on R and f: lighter load (larger R) requires larger inductance to maintain CCM; higher frequency reduces L_crit.
Example: R=50Ω, D=0.5, f=10kHz → L_crit = 50×0.5/(2×10000) = 1.25mH. Current setting L=1.2mH < L_crit, right at DCM boundary. Try changing L to 2mH to see mode transition.
Design insight: to maintain CCM under all load conditions, choose an inductance satisfying L > L_crit at the lightest load. But larger inductance means larger size and slower transient response — another engineering tradeoff.
Critical Inductance Boundary
R=50Ω, L=1.2mH (L_crit=1.25mH). Right at the CCM/DCM boundary.
After reading this section, run the simulation and observe the waveforms. To explore further, open the example in a standalone page.
Watch Items
- Current L=1.2mH: i_l1 just touches zero — CCM/DCM boundary
- Change L to 2mH and re-run: current no longer reaches zero, enters CCM